# Functional dependence between two variables

*Functional dependence. Argument ( independent variable ).*

Function. Single-valued function. Multiple-valued function.

Function. Single-valued function. Multiple-valued function.

Two variables *x *and* y* are tied by a *functional dependence*, if for each value of one of them it is possible to receive by the certain

rule one or some values of another.

E x a m p l e . | A temperature T of water boiling and atmosphere pressure p are tied bya functional dependence, because each value of pressure corresponds to a certain value of the temperature and inversely. So, if p = 1 bar, then T = 100°C; if p = 0.5 bar, then T = 81.6°C. |

A variable, values of which are given, is called an *argument* or an *independent* variable; the other variable, values of which are

found by the certain rule is called a *function. * Usually an argument is marked as *x*, and a function is marked as * y *.

If only one value of function corresponds to each value of argument, this function is called a *single-valued * *function*;

otherwise, if there are many corresponding values, this function is called a *multiple-valued function* ( two-valued, three-valued and etc.).

E x a m p l e . | A body is thrown upwards; h is its height over a ground, t is the time, passedfrom a throwing moment. h is a single-valued function of t, but t is atwo-valued function of h, because the body is on the same height twice: the first time at an assent, the second time at a fall. The formula
binding variables |